Skip to main content
SpringerLink
Log in
Book cover

Nonlinear Ultrasonic and Vibro-Acoustical Techniques for Nondestructive Evaluation pp 103–137Cite as

Modeling and Numerical Simulations in Nonlinear Acoustics Used for Damage Detection

  • Chapter
  • First Online:

Abstract

Structural damage detection is frequently accomplished by interrogation with elastic waves.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   299.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   299.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. T. Stepinski, T. Uhl, W.J. Staszewski, Advanced Structural Damage Detection: From Theory to Engineering Applications, 1st edn. (Wiley, Chichester, 2013)

    Book  Google Scholar 

  2. C. Boller, F.-K. Chang, Y. Fujino, Encyclopedia of Structural Health Monitoring (Wiley, Chichester, 2009)

    Book  Google Scholar 

  3. A.N. Norris, Finite-amplitude waves in solids, in Nonlinear Acoustics, ed. by M.F. Hamilton, D.T. Blackstock (Academic Press, San Diego, 1998), pp. 263–277

    Google Scholar 

  4. N. Rauter, R. Lammering, Numerical simulation of elastic wave propagation in isotropic media considering material and geometrical nonlinearities. Smart Mater. Struct. 24(4), 045027 (2015)

    Article  Google Scholar 

  5. V.K. Chillara, C.J. Lissenden, Review of nonlinear ultrasonic guided wave nondestructive evaluation: theory, numerics and experiments. Opt. Eng. 55(1), 011002 (2015)

    Article  Google Scholar 

  6. K.-Y. Jhang, Nonlinear ultrasonic techniques for nondestructive assessment of micro damage in material: a review. Int. J. Precis. Eng. Manuf. 10(1), 123–135 (2009)

    Article  Google Scholar 

  7. M. Destrade, R.W. Ogden, On the third- and fourth-order constants of incompressible isotropic elasticity. J. Acoust. Soc. Am. 128, 3334–3343 (2010)

    Article  Google Scholar 

  8. M. Muller, A. Sutin, R. Guyer, M. Talmant, P. Laugier, P.A. Johnson, Nonlinear resonant ultrasound spectroscopy (nrus) applied to damage assessment in bone. J. Acoust. Soc. Am. 118(6), 3946–3952 (2005)

    Article  Google Scholar 

  9. W.J.N. de Lima, M.F. Hamilton, Finite-amplitude waves in isotropic elastic plates. J. Sound Vib. 265, 819–839 (2003)

    Article  Google Scholar 

  10. A. Klepka, W.J. Staszewski, R.B. Jenal, M. Szwedo, J. Iwaniec, Nonlinear acoustics for fatigue crack detection - experimental investigations of vibroacoustic wave modulations. Struct. Health Monit. 11, 197–211 (2012)

    Article  Google Scholar 

  11. R. Radecki, Z. Su, L. Cheng, P. Packo, W.J. Staszewski, Modelling nonlinearity of guided ultrasonic waves in fatigued materials using a nonlinear local interaction simulation approach and a spring model. Ultrasonics. 84, 272–289 (2008). https://doi.org/10.1016/j.ultras.2017.11.008

    Article  Google Scholar 

  12. G.B. Santoni, L. Yu, B. Xu, V. Giurgiutiu, Lamb wave-mode tuning of piezoelectric wafer active sensors for structural health monitoring. J. Vib. Acoust. 129(6), 752–762 (2007)

    Article  Google Scholar 

  13. P.Y. Moghadam, N. Quaegebeur, P. Masson, Mode selective generation of guided waves by systematic optimization of the interfacial shear stress profile. Smart Mater. Struct. 24(1), 015003 (2015)

    Article  Google Scholar 

  14. P. Packo, T. Bielak, A.B. Spencer, W.J. Staszewski, T. Uhl, K. Worden, Lamb wave propagation modelling and simulation using parallel processing architecture and graphical cards. Smart Mater. Struct. 21(7), 075001 (2012)

    Article  Google Scholar 

  15. P. Packo, T. Bielak, A.B. Spencer, T. Uhl, W.J. Staszewski, K. Worden, T. Barszcz, P. Russek, K. Wiatr, Numerical simulations of elastic wave propagation using graphical processing units—comparative study of high-performance computing capabilities. Comput. Methods Appl. Mech. Eng. 290, 98–126 (2015)

    Article  MathSciNet  Google Scholar 

  16. G. Noh, S. Ham, K.-J. Bathe, Performance of an implicit time integration scheme in the analysis of wave propagations. Comput. Struct. 123, 93–105 (2013)

    Article  Google Scholar 

  17. K.-T. Kim, K.-J. Bathe, Transient implicit wave propagation dynamics with the method of finite spheres. Comput. Struct. 173, 50–60 (2016)

    Article  Google Scholar 

  18. J.C. Strickwerda, Finite Difference Schemes and Partial Differential Equations (Wadsworth-Brooks, Belmont, 1989)

    Google Scholar 

  19. J. Virieux, P-sv wave propagation in heterogeneous media: velocity-stress finite difference method. Geophysics 51, 889–901 (1986)

    Article  Google Scholar 

  20. P. Fellinger, R. Marklein, K.J. Langenberg, S. Klaholz, Numerical modeling of elastic wave propagation and scattering with efit - elastodynamic finite integration technique. Wave Motion 21(1), 47–66 (1995)

    Article  Google Scholar 

  21. P.P. Delsanto, R.S. Schechter, H.H. Chaskelis, R.B. Mignogna, R. Kline, Connection machine simulation of ultrasonic wave propagation in materials. II: the two-dimensional case. Wave Motion 20(4), 295–314 (1994)

    MATH  Google Scholar 

  22. P. Packo, R. Radecki, P. Kijanka, W.J. Staszewski, T. Uhl, M.J. Leamy, Local numerical modelling of ultrasonic guided waves in linear and nonlinear media, in Proceedings of SPIE Health Monitoring of Structural and Biological Systems 2017, vol. 10170 (2017), pp. 1017023–1017023-10

    Google Scholar 

  23. M.J. Leamy, Application of cellular automata modeling to seismic elastodynamics. Int. J. Solids Struct. 45(17), 4835–4849 (2008)

    Article  Google Scholar 

  24. R.K. Hopman, M.J. Leamy, Triangular cellular automata for computing two-dimensional elastodynamic response on arbitrary domains. J. Appl. Mech. 78(2), 021020 (2011)

    Article  Google Scholar 

  25. M.J. Leamy, T.B. Autrusson, W.J. Staszewski, T. Uhl, P. Packo, Local computational strategies for predicting wave propagation in nonlinear media, in Proceedings of SPIE Health Monitoring of Structural and Biological Systems 2014, vol. 9064 (2014), pp. 90641J–90641J-15

    Google Scholar 

  26. K.J. Bathe, Finite Element Procedures in Engineering Analysis (Prentice-Hall, Englewood Cliff, 1982)

    Google Scholar 

  27. O.C. Zienkiewicz, The Finite Element Method (McGraw-Hill, London, 1989)

    Google Scholar 

  28. A.A. Becker, The Boundary Element Method in Engineering: A Complete Course (McGraw-Hill, London, 1992)

    Google Scholar 

  29. A.T. Patera, A spectral element method for fluid dynamics: laminar flow in a channel expansion. J. Comput. Phys. 54(3), 468–488 (1984)

    Article  Google Scholar 

  30. S. Gopalakrishnan, A. Chakraborty, D.R. Mahapatra, Spectral Finite Element Method (Springer, Berlin, 2008)

    MATH  Google Scholar 

  31. S. Ham, K.J. Bathe, A finite element method enriched for wave propagation problems. Comput. Struct. 94–95, 1–12 (2012)

    Article  Google Scholar 

  32. P. Packo, T. Uhl, W.J. Staszewski, Generalized semi-analytical finite difference method for dispersion curves calculation and numerical dispersion analysis for Lamb waves. J. Acoust. Soc. Am. 136(3), 993 (2014)

    Article  Google Scholar 

  33. P. Kijanka, W.J. Staszewski, P. Packo, Simulation of guided wave propagation near numerical brillouin zones, in Proceedings of SPIE Health Monitoring of Structural and Biological Systems 2016, vol. 9805 (2016), pp. 98050Q–98050Q-6

    Google Scholar 

  34. D. Broda, W.J. Staszewski, A. Martowicz, T. Uhl, V.V. Silberschmidt, Modelling of nonlinear crack–wave interactions for damage detection based on ultrasound—a review. J. Sound Vib. 333(4), 1097–1118 (2014)

    Article  Google Scholar 

  35. L.D. Landau, E.M. Lifshitz, Theory of Elasticity, 2nd edn. (Pergamon Press, Oxford, 1970)

    MATH  Google Scholar 

  36. V. Gusev, V. Tournat, B. Castagnede, Nonlinear acoustic phenomena in micro-inhomogeneous media, in Materials and Acoustic Handbook, ed. by C. Potel, M. Bruneau (ISTE Ltd, London, 2009)

    MATH  Google Scholar 

  37. K. Worden, G.R. Tomlinson, Nonlinearity in Structural Dynamics: Detection, Identification and Modelling (IoP, Bristol, 2001)

    Google Scholar 

  38. R. Ruotolo, C. Surace, P. Crespo, D. Storer, Harmonic analysis of the vibrations of a cantilevered beam with a closing crack. Comput. Struct. 61(6), 1057–1074 (1996)

    Article  Google Scholar 

  39. T.G. Chondros, A.D. Dimarogonas, J. Yao, Vibrations of a beam with a breathing crack. J. Sound Vib. 239(1), 57–67 (2001)

    Article  Google Scholar 

  40. M.I. Friswell, J.E.T. Penny, Crack modeling for structural health monitoring. Struct. Health Monit. 1(2), 139–148 (2002)

    Article  Google Scholar 

  41. I.Y. Solodov, N. Krohn, G. Busse, CAN: an example of nonclassical acoustic nonlinearity in solids. Ultrasonics 40(1–8), 621–625 (2002)

    Article  Google Scholar 

  42. I.Y. Solodov, N. Krohn, G. Busse, Nonlinear ultrasonic NDT for early defect recognition and imaging, in Proceedings of the 10th European Conference on Non-destructive Testing, Moscow (2010)

    Google Scholar 

  43. F. Semperlotti, K.W. Wang, E.C. Smith, Localization of a breathing crack using super-harmonic signals due to system nonlinearity. AIAA J. 47(9), 2076–2086 (2009)

    Article  Google Scholar 

  44. V.E. Nazarov, L.A. Ostrovsky, I.A. Soustova, A.M. Sutin, Nonlinear acoustics of micro-inhomogeneous media. Phys. Earth Planet. Inter. 50(1), 65–73 (1988)

    Article  Google Scholar 

  45. V.E. Nazarov, A.V. Radostin, L.A. Ostrovsky, I.A. Soustova, Wave processes in media with hysteretic nonlinearity. Part I. Acoust. Phys. 49(3), 344–355 (2003)

    Article  Google Scholar 

  46. K.R. McCall, R.A. Guyer, Equation of state and wave propagation in hysteretic nonlinear elastic materials. J. Geophys. Res. Solid Earth 99(B12), 23887–23897 (1994)

    Article  Google Scholar 

  47. R.A. Guyer, K.R. McCall, G.N. Boitnott, Hysteresis, discrete memory, and nonlinear wave propagation in rock: a new paradigm. Phys. Rev. Lett. 74, 3491–3494 (1995)

    Article  Google Scholar 

  48. L.A. Ostrovsky, S.N. Gurbatov, J.N. Didenkulov, Nonlinear acoustics in nizhni novgorod (a review). Acoust. Phys. 51(2), 114–127 (2005)

    Article  Google Scholar 

  49. I.Y. Belyaeva, V.Y. Zaitsev, L.A. Ostrovsky, Nonlinear acousto-elastic properties of granular media. Acoust. Phys. 39(1), 11–14 (1993)

    Google Scholar 

  50. V. Zaitsev, P. Sas, Dissipation in microinhomogeneous solids: inherent amplitude-dependent losses of a non-hysteretical and non-frictional type. Acta Acust. united Ac. 86(3), 429–445 (2000)

    Google Scholar 

  51. V.Y. Zaitsev, V. Gusev, B. Castagnède, Observation of the “luxemburg–gorky effect” for elastic waves. Ultrasonics 40(1), 627–631 (2002)

    Article  Google Scholar 

  52. J. Lemaitre, R. Desmorat, Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures (Springer, Berlin, 2005)

    Google Scholar 

  53. J. Rushchitsky, Nonlinear Elastic Waves in Materials (Springer, Berlin, 2014)

    Book  Google Scholar 

  54. A. Jeffrey, J. Engelbrecht, Nonlinear Waves in Solids. CISM Courses and Lectures (Springer, Berlin, 1994)

    Book  Google Scholar 

  55. A.F. Bower, Applied Mechanics of Solids (CRC Press, Boca Raton, 2010)

    Google Scholar 

  56. M. Destrade, G. Saccomandi, M. Vianello, Proper formulation of viscous dissipation for nonlinear waves in solids. Acoust. Soc. Am. J. 133, 1255 (2013)

    Article  Google Scholar 

  57. P. Packo, Numerical simulation of elasticwave propagation, in Advanced Structural Damage Detection: From Theory to Engineering Applications (Wiley, Chichester, 2013)

    Google Scholar 

  58. R. Courant, K. Friedrichs, H. Lewy, Über die partiellen differenzengleichungen der mathematischen physik. Math. Ann. 100(1), 32–74 (1928)

    Article  MathSciNet  Google Scholar 

  59. Y. Shen, C.E.S. Cesnik, Modeling of nonlinear interactions between guided waves and fatigue cracks using local interaction simulation approach. Ultrasonics 74, 106–123 (2017)

    Article  Google Scholar 

  60. P.P. Delsanto, T. Whitcombe, H.H. Chaskelis, R.B. Mignogna, Connection machine simulation of ultrasonic wave propagation in materials. I: the one-dimensional case. Wave Motion 16(1), 65–80 (1992)

    Google Scholar 

  61. P. Packo, T. Bielak, A.B. Spencer, W.J. Staszewski, T. Uhl, K. Worden, Lamb wave propagation modelling and simulation using parallel processing architecture and graphical cards. Smart Mater. Struct. 21(7), 075001 (2012)

    Article  Google Scholar 

  62. P. Packo, T. Bielak, A.B. Spencer, T. Uhl, W.J. Staszewski, K. Worden, T. Barszcz, P. Russek, K. Wiatr, Numerical simulations of elastic wave propagation using graphical processing units—comparative study of high-performance computing capabilities. Comput. Methods Appl. Mech. Eng. 290, 98–126 (2015)

    Article  MathSciNet  Google Scholar 

  63. D. Dutta, H. Sohn, K.A. Harries, P. Rizzo, A nonlinear acoustic technique for crack detection in metallic structures. Struct. Health Monit. 8(3), 251–262 (2009)

    Article  Google Scholar 

  64. M. Deng, Analysis of second-harmonic generation of lamb modes using a modal analysis approach. J. Appl. Phys. 94(6), 4152–4159 (2003)

    Article  Google Scholar 

  65. C. Zhou, M. Hong, Z. Su, Q. Wang, L. Cheng, Evaluation of fatigue cracks using nonlinearities of acousto-ultrasonic waves acquired by an active sensor network. Smart Mater. Struct. 22(1), 015018 (2013)

    Article  Google Scholar 

  66. I. Solodov, J. Wackerl, K. Pfleiderer, G. Busse, Nonlinear self-modulation and subharmonic acoustic spectroscopy for damage detection and location. Appl. Phys. Lett. 84(26), 5386–5388 (2004)

    Article  Google Scholar 

  67. F. Aymerich, W.J. Staszewski, Experimental study of impact-damage detection in composite laminates using a cross-modulation vibro-acoustic technique. Struct. Health Monit. 9(6), 541–553 (2010)

    Article  Google Scholar 

  68. D.T. Zeitvogel, K.H. Matlack, J.-Y. Kim, L.J. Jacobs, P.M. Singh, J. Qu, Characterization of stress corrosion cracking in carbon steel using nonlinear rayleigh surface waves. NDT & E Int. 62, 144–152 (2014)

    Article  Google Scholar 

  69. J.-Y. Kim, V.A. Yakovlev, S.I. Rokhlin, Parametric modulation mechanism of surface acoustic wave on a partially closed crack. Appl. Phys. Lett. 82(19), 3203–3205 (2003)

    Article  Google Scholar 

  70. T. Stratoudaki, R. Ellwood, S. Sharples, M. Clark, M.G. Somekh, I.J. Collison, Measurement of material nonlinearity using surface acoustic wave parametric interaction and laser ultrasonics. J. Acoust. Soc. Am. 129(4), 1721–1728 (2011)

    Article  Google Scholar 

  71. Y. Shen, V. Giurgiutiu, Predictive modeling of nonlinear wave propagation for structural health monitoring with piezoelectric wafer active sensors. J. Intell. Mater. Syst. Struct. 25(4), 506–520 (2014)

    Article  Google Scholar 

  72. T.J.R. Hughes, R.L. Taylor, J.L. Sackman, A. Curnier, W. Kanoknukulchai, A finite element method for a class of contact-impact problems. Comput. Methods Appl. Mech. Eng. 8(3), 249–276 (1976)

    Article  Google Scholar 

  73. M.B. Obenchain, K.S. Nadella, C.E.S. Cesnik, Hybrid global matrix/local interaction simulation approach for wave propagation in composites. AIAA J. 53(2), 379–393 (2015)

    Article  Google Scholar 

  74. A. Martowicz, P. Packo, W.J. Staszewski, T. Uhl, Modelling of nonlinear vibro–acoustic wave interaction in cracked aluminium plates using local interaction simulation approach, in 6th European Congress on Computational Methods in Applied Sciences and Engineering, Vienna, Austria (2012)

    Google Scholar 

  75. P.P. Delsanto, M. Scalerandi, A spring model for the simulation of the propagation of ultrasonic pulses through imperfect contact interfaces. J. Acoust. Soc. Am. 104(5), 2584–2591 (1998)

    Article  Google Scholar 

  76. M. Scalerandi, V. Agostini, P.P. Delsanto, K. Van Den Abeele, P.A. Johnson, Local interaction simulation approach to modelling nonclassical, nonlinear elastic behavior in solids. J. Acoust. Soc. Am. 113(6), 3049–3059 (2003)

    Article  Google Scholar 

  77. P. Kijanka, R. Radecki, P. Packo, W.J. Staszewski, T. Uhl, M.J. Leamy, Nonlinear dispersion effects in elastic plates: numerical modelling and validation, in Proceedings of SPIE Health Monitoring of Structural and Biological Systems 2017, vol. 10170 (2017), pp. 101701U–101701U-8

    Google Scholar 

  78. P. Packo, T. Uhl, W.J. Staszewski, M.J. Leamy, Amplitude-dependent lamb wave dispersion in nonlinear plates. J. Acoust. Soc. Am. 140(2), 1319–1331 (2016)

    Article  Google Scholar 

  79. M.F. Müller, J.-Y. Kim, J. Qu, L.J. Jacobs, Characteristics of second harmonic generation of lamb waves in nonlinear elastic plates. J. Acoust. Soc. Am. 127(4), 2141–2152 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Robotics and Mechatronics, AGH University of Science and Technology, Kraków, Poland

    Pawel Packo, Rafal Radecki, Tadeusz Uhl & Wieslaw J. Staszewski

  2. School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Michael J. Leamy

Authors
  1. Pawel Packo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rafal Radecki
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael J. Leamy
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tadeusz Uhl
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Wieslaw J. Staszewski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pawel Packo .

Editor information

Editors and Affiliations

  1. Department of Civil Engineering and Engineering Mechanics, Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ, USA

    Tribikram Kundu

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Packo, P., Radecki, R., Leamy, M.J., Uhl, T., Staszewski, W.J. (2019). Modeling and Numerical Simulations in Nonlinear Acoustics Used for Damage Detection. In: Kundu, T. (eds) Nonlinear Ultrasonic and Vibro-Acoustical Techniques for Nondestructive Evaluation. Springer, Cham. https://doi.org/10.1007/978-3-319-94476-0_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-94476-0_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94474-6

  • Online ISBN: 978-3-319-94476-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation